A structured algorithm for minimum l∞-norm solutions and its application to a robot velocity workspace analysis

Abstract

Herein is proposed a concise algorithmic procedure for deriving a minimum l∞-norm solution of the system of consistent linear equations Ax=b, where A is a m×n matrix, b is given as a m×1 vector and x is a n×1 unknown vector. The proposed algorithm is developed based on the geometrical analysis of the characteristics of the minimum infinity-norm solution. The proposed algorithm is well-structured so that it may be implemented easily through simple linear algebraic manipulation. For the case of n>m, the basic idea of the method is extended to finding internally mapped vertices when a n dimensional polytope is transformed into m dimensional polytope through consistent linear mapping A. The proposed method is applied to the task velocity analysis for robot manipulators with joint velocity constraints.